{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# How to use backpropagation to train a feedforward NN"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This noteboo implements a simple single-layer architecture and forward propagation computations using matrix algebra and Numpy,the Python counterpart of linear algebra.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Please follow the installations [instructions](../installation.md)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imports & Settings "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:41.038452Z",
     "start_time": "2020-06-21T17:35:41.036381Z"
    }
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:41.615448Z",
     "start_time": "2020-06-21T17:35:41.039671Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "from pathlib import Path\n",
    "from copy import deepcopy\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import sklearn\n",
    "from sklearn.datasets import make_circles\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.colors import ListedColormap\n",
    "from mpl_toolkits.mplot3d import Axes3D  # 3D plots\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:41.620335Z",
     "start_time": "2020-06-21T17:35:41.617256Z"
    }
   },
   "outputs": [],
   "source": [
    "# plotting style\n",
    "sns.set_style('white')\n",
    "# for reproducibility\n",
    "np.random.seed(seed=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:41.637394Z",
     "start_time": "2020-06-21T17:35:41.621735Z"
    }
   },
   "outputs": [],
   "source": [
    "results_path = Path('results')\n",
    "if not results_path.exists():\n",
    "    results_path.mkdir()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Input Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate random data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The target `y` represents two classes generated by two circular distribution that are not linearly separable because class 0 surrounds class 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will generate 50,000 random samples in the form of two concentric circles with different radius using scikit-learn's make_circles function so that the classes are not linearly separable. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:41.645750Z",
     "start_time": "2020-06-21T17:35:41.639129Z"
    }
   },
   "outputs": [],
   "source": [
    "# dataset params\n",
    "N = 50000\n",
    "factor = 0.1\n",
    "noise = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:41.653568Z",
     "start_time": "2020-06-21T17:35:41.646974Z"
    }
   },
   "outputs": [],
   "source": [
    "n_iterations = 50000\n",
    "learning_rate = 0.0001\n",
    "momentum_factor = .5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:41.670047Z",
     "start_time": "2020-06-21T17:35:41.654742Z"
    }
   },
   "outputs": [],
   "source": [
    "# generate data\n",
    "X, y = make_circles(\n",
    "    n_samples=N,\n",
    "    shuffle=True,\n",
    "    factor=factor,\n",
    "    noise=noise)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:41.675414Z",
     "start_time": "2020-06-21T17:35:41.671399Z"
    }
   },
   "outputs": [],
   "source": [
    "# define outcome matrix\n",
    "Y = np.zeros((N, 2))\n",
    "for c in [0, 1]:\n",
    "    Y[y == c, c] = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$X =\\begin{bmatrix} \n",
    "x_{11} & x_{12} \\\\\n",
    "\\vdots & \\vdots \\\\\n",
    "x_{N1} & x_{N2}\n",
    "\\end{bmatrix}\n",
    "\\quad\\quad\n",
    "Y = \\begin{bmatrix} \n",
    "y_{11} & y_{12}\\\\\n",
    "\\vdots & \\vdots \\\\\n",
    "y_{N1} & y_{N2} \n",
    "\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:41.685463Z",
     "start_time": "2020-06-21T17:35:41.676786Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Shape of: X: (50000, 2) | Y: (50000, 2) | y: (50000,)'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f'Shape of: X: {X.shape} | Y: {Y.shape} | y: {y.shape}'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualize Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:42.826013Z",
     "start_time": "2020-06-21T17:35:41.686593Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.scatterplot(x=X[:, 0], \n",
    "                y=X[:, 1], \n",
    "                hue=y,\n",
    "               style=y,\n",
    "               markers=['_', '+'])\n",
    "ax.set_title('Synthetic Classification Data')\n",
    "sns.despine()\n",
    "plt.tight_layout()\n",
    "plt.savefig(results_path / 'ffnn_data', dpi=300);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neural Network Architecture"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hidden Layer Activations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The hidden layer $h$ projects the 2D input into a 3D space. To this end, the hidden layer weights are a $2\\times3$ matrix $\\mathbf{W}^h$, and the hidden layer bias vector $\\mathbf{b}^h$ is a 3-dimensional vector:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align*}\n",
    "\\underset{\\scriptscriptstyle 2 \\times 3}{\\mathbf{W}^h} =\n",
    "\\begin{bmatrix} \n",
    "w^h_{11} & w^h_{12} & w^h_{13} \\\\\n",
    "w^h_{21} & w^h_{22} & w^h_{23}\n",
    "\\end{bmatrix}\n",
    "&& \\underset{\\scriptscriptstyle 1 \\times 3}{\\mathbf{b}^h} = \n",
    "\\begin{bmatrix} \n",
    "b^h_1 & b^h_2 & b^h_3\n",
    "\\end{bmatrix}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output layer values $\\mathbf{Z}^h$ result from the dot product of the $N\\times\\ 2$ input data $\\mathbf{X}$ and the the $2\\times3$ weight matrix $\\mathbf{W}^h$ and the addition of the $1\\times3$ hidden layer bias vector $\\mathbf{b}^h$:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\underset{\\scriptscriptstyle N \\times 3}{\\mathbf{Z}^h} = \\underset{\\scriptscriptstyle N \\times 2}{\\vphantom{\\mathbf{W}^o}\\mathbf{X}}\\cdot\\underset{\\scriptscriptstyle 2 \\times 3}{\\mathbf{W}^h} + \\underset{\\scriptscriptstyle 1 \\times 3}{\\mathbf{b}^h}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The logistic sigmoid function $\\sigma$ applies a non-linear transformation to $\\mathbf{Z}^h$ to yield  the hidden layer activations as an $N\\times3$ matrix:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\underset{\\scriptscriptstyle N \\times 3}{\\mathbf{H}} = \\sigma(\\mathbf{X} \\cdot \\mathbf{W}^h + \\mathbf{b}^h) = \\frac{1}{1+e^{−(\\mathbf{X} \\cdot \\mathbf{W}^h + \\mathbf{b}^h)}} = \\begin{bmatrix} \n",
    "h_{11} & h_{12} & h_{13} \\\\\n",
    "\\vdots & \\vdots & \\vdots \\\\\n",
    "h_{N1} & h_{N2} & h_{N3}\n",
    "\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:42.830335Z",
     "start_time": "2020-06-21T17:35:42.827441Z"
    }
   },
   "outputs": [],
   "source": [
    "def logistic(z):\n",
    "    \"\"\"Logistic function.\"\"\"\n",
    "    return 1 / (1 + np.exp(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:42.845494Z",
     "start_time": "2020-06-21T17:35:42.831576Z"
    }
   },
   "outputs": [],
   "source": [
    "def hidden_layer(input_data, weights, bias):\n",
    "    \"\"\"Compute hidden activations\"\"\"\n",
    "    return logistic(input_data @ weights + bias)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Output Activations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The values $\\mathbf{Z}^o$ for the output layer $o$ are a $N\\times2$ matrix that results from the dot product of the $\\underset{\\scriptscriptstyle N \\times 3}{\\mathbf{H}}$ hidden layer activation matrix with the $3\\times2$ output weight matrix $\\mathbf{W}^o$ and the addition of the $1\\times2$ output bias vector $\\mathbf{b}^o$:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\underset{\\scriptscriptstyle N \\times 2}{\\mathbf{Z}^o} = \\underset{\\scriptscriptstyle N \\times 3}{\\vphantom{\\mathbf{W}^o}\\mathbf{H}}\\cdot\\underset{\\scriptscriptstyle 3 \\times 2}{\\mathbf{W}^o} + \\underset{\\scriptscriptstyle 1 \\times 2}{\\mathbf{b}^o}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-10T13:39:58.307221Z",
     "start_time": "2019-01-10T13:39:58.295854Z"
    }
   },
   "source": [
    "The Softmax function $\\varsigma$ squashes the unnormalized probabilities predicted for each class  to lie within $[0, 1]$ and sum to 1.  The result is a $N\\times2$ matrix with one column for each output class."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\underset{\\scriptscriptstyle N \\times 2}{\\mathbf{\\hat{Y}}} \n",
    "= \\varsigma(\\mathbf{H} \\cdot \\mathbf{W}^o + \\mathbf{b}^o)\n",
    "= \\frac{e^{Z^o}}{\\sum_{c=1}^C e^{\\mathbf{z}^o_c}}\n",
    "= \\frac{e^{H \\cdot W^o + \\mathbf{b}^o}}{\\sum_{c=1}^C e^{H \\cdot \\mathbf{w}^o_c + b^o_c}}\n",
    "= \\begin{bmatrix} \n",
    "\\hat{y}_{11} & \\hat{y}_{12}\\\\\n",
    "\\vdots & \\vdots \\\\\n",
    "\\hat{y}_{n1} & \\hat{y}_{n2} \n",
    "\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:42.852708Z",
     "start_time": "2020-06-21T17:35:42.848074Z"
    }
   },
   "outputs": [],
   "source": [
    "def softmax(z):\n",
    "    \"\"\"Softmax function\"\"\"\n",
    "    return np.exp(z) / np.sum(np.exp(z), axis=1, keepdims=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:42.863907Z",
     "start_time": "2020-06-21T17:35:42.854076Z"
    }
   },
   "outputs": [],
   "source": [
    "def output_layer(hidden_activations, weights, bias):\n",
    "    \"\"\"Compute the output y_hat\"\"\"\n",
    "    return softmax(hidden_activations @ weights + bias)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Forward Propagation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `forward_prop` function combines the previous operations to yield the output activations from the  input data as a function of weights and biases. The `predict` function produces the binary class predictions given weights, biases, and input data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:42.879687Z",
     "start_time": "2020-06-21T17:35:42.865061Z"
    }
   },
   "outputs": [],
   "source": [
    "def forward_prop(data, hidden_weights, hidden_bias, output_weights, output_bias):\n",
    "    \"\"\"Neural network as function.\"\"\"\n",
    "    hidden_activations = hidden_layer(data, hidden_weights, hidden_bias)\n",
    "    return output_layer(hidden_activations, output_weights, output_bias)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:42.887589Z",
     "start_time": "2020-06-21T17:35:42.880669Z"
    }
   },
   "outputs": [],
   "source": [
    "def predict(data, hidden_weights, hidden_bias, output_weights, output_bias):\n",
    "    \"\"\"Predicts class 0 or 1\"\"\"\n",
    "    y_pred_proba = forward_prop(data,\n",
    "                                hidden_weights,\n",
    "                                hidden_bias,\n",
    "                                output_weights,\n",
    "                                output_bias)\n",
    "    return np.around(y_pred_proba)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cross-Entropy Loss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cost function $J$ uses the cross-entropy loss $\\xi$ that sums the deviations of the predictions for each class $c$  $\\hat{y}_{ic}, i=1,...,N$ from the actual outcome."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$J(\\mathbf{Y},\\mathbf{\\hat{Y}}) = \\sum_{i=1}^n \\xi(\\mathbf{y}_i,\\mathbf{\\hat{y}}_i) = − \\sum_{i=1}^N \\sum_{i=c}^{C} y_{ic} \\cdot log(\\hat{y}_{ic})$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:42.895481Z",
     "start_time": "2020-06-21T17:35:42.888958Z"
    }
   },
   "outputs": [],
   "source": [
    "def loss(y_hat, y_true):\n",
    "    \"\"\"Cross-entropy\"\"\"\n",
    "    return - (y_true * np.log(y_hat)).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Backpropagation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Backpropagation updates parameters values based on the partial derivative of the loss with respect to that parameter, computed using the chain rule."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loss Function Gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The derivative of the loss function $J$ with respect to each output layer activation $\\varsigma(\\mathbf{Z}^o_i), i=1,...,N$, is a very simple expression:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\frac{\\partial J}{\\partial z^0_i} = \\delta^o = \\hat{y}_i-y_i$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See [here](https://math.stackexchange.com/questions/945871/derivative-of-softmax-loss-function) and [here](https://deepnotes.io/softmax-crossentropy) for details on derivation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:42.903975Z",
     "start_time": "2020-06-21T17:35:42.896789Z"
    }
   },
   "outputs": [],
   "source": [
    "def loss_gradient(y_hat, y_true):\n",
    "    \"\"\"output layer gradient\"\"\"\n",
    "    return y_hat - y_true"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Output Layer Gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Output Weight Gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To propagate the updates back to the output layer weights, we take the partial derivative of the loss function with respect to the weight matrix:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-08T04:18:37.478549Z",
     "start_time": "2019-01-08T04:18:37.476003Z"
    }
   },
   "source": [
    "$$\n",
    "\\frac{\\partial J}{\\partial \\mathbf{W}^o} = H^T \\cdot (\\mathbf{\\hat{Y}}-\\mathbf{Y}) = H^T \\cdot \\delta^{o}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:42.912049Z",
     "start_time": "2020-06-21T17:35:42.905042Z"
    }
   },
   "outputs": [],
   "source": [
    "def output_weight_gradient(H, loss_grad):\n",
    "    \"\"\"Gradients for the output layer weights\"\"\"\n",
    "    return  H.T @ loss_grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Output Bias Update"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To update the output layer bias values, we similarly apply the chain rule to obtain the partial derivative of the loss function with respect to the bias vector:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\frac{\\partial J}{\\partial \\mathbf{b}_{o}} \n",
    "= \\frac{\\partial \\xi}{\\partial \\mathbf{\\hat{Y}}} \\frac{\\partial \\mathbf{\\hat{Y}}}{\\partial \\mathbf{Z}^o}  \\frac{\\partial \\mathbf{Z}^{o}}{\\partial \\mathbf{b}^o}\n",
    "= \\sum_{i=1}^N 1 \\cdot (\\mathbf{\\hat{y}}_i - \\mathbf{y}_i) \n",
    "= \\sum_{i=1}^N \\delta_{oi}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:42.921767Z",
     "start_time": "2020-06-21T17:35:42.913003Z"
    }
   },
   "outputs": [],
   "source": [
    "def output_bias_gradient(loss_grad):\n",
    "    \"\"\"Gradients for the output layer bias\"\"\"\n",
    "    return np.sum(loss_grad, axis=0, keepdims=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hidden layer gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\delta_{h} \n",
    "= \\frac{\\partial J}{\\partial \\mathbf{Z}^h} \n",
    "= \\frac{\\partial J}{\\partial \\mathbf{H}} \\frac{\\partial \\mathbf{H}}{\\partial \\mathbf{Z}^h} \n",
    "= \\frac{\\partial J}{\\partial \\mathbf{Z}^o} \\frac{\\partial \\mathbf{Z}^o}{\\partial H} \\frac{\\partial H}{\\partial \\mathbf{Z}^h}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:42.932445Z",
     "start_time": "2020-06-21T17:35:42.923415Z"
    }
   },
   "outputs": [],
   "source": [
    "def hidden_layer_gradient(H, out_weights, loss_grad):\n",
    "    \"\"\"Error at the hidden layer.\n",
    "    H * (1-H) * (E . Wo^T)\"\"\"\n",
    "    return H * (1 - H) * (loss_grad @ out_weights.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Hidden Weight Gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\frac{\\partial J}{\\partial \\mathbf{W}^h} = \\mathbf{X}^T \\cdot \\delta^{h}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:42.941869Z",
     "start_time": "2020-06-21T17:35:42.933726Z"
    }
   },
   "outputs": [],
   "source": [
    "def hidden_weight_gradient(X, hidden_layer_grad):\n",
    "    \"\"\"Gradient for the weight parameters at the hidden layer\"\"\"\n",
    "    return X.T @ hidden_layer_grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Hidden Bias Gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-01-08T04:24:55.165112Z",
     "start_time": "2019-01-08T04:24:55.161087Z"
    }
   },
   "source": [
    "$$\n",
    "\\frac{\\partial \\xi}{\\partial \\mathbf{b}_{h}} \n",
    "= \\frac{\\partial \\xi}{\\partial H} \\frac{\\partial H}{\\partial Z_{h}} \\frac{\\partial Z_{h}}{\\partial \\mathbf{b}_{h}}\n",
    "= \\sum_{j=1}^N \\delta_{hj}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:42.949962Z",
     "start_time": "2020-06-21T17:35:42.943349Z"
    }
   },
   "outputs": [],
   "source": [
    "def hidden_bias_gradient(hidden_layer_grad):\n",
    "    \"\"\"Gradient for the bias parameters at the output layer\"\"\"\n",
    "    return np.sum(hidden_layer_grad, axis=0, keepdims=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialize Weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:42.957689Z",
     "start_time": "2020-06-21T17:35:42.950920Z"
    }
   },
   "outputs": [],
   "source": [
    "def initialize_weights():\n",
    "    \"\"\"Initialize hidden and output weights and biases\"\"\"\n",
    "\n",
    "    # Initialize hidden layer parameters\n",
    "    hidden_weights = np.random.randn(2, 3)\n",
    "    hidden_bias = np.random.randn(1, 3)\n",
    "\n",
    "    # Initialize output layer parameters\n",
    "    output_weights = np.random.randn(3, 2)\n",
    "    output_bias = np.random.randn(1, 2)\n",
    "    return hidden_weights, hidden_bias, output_weights, output_bias"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute Gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:42.968582Z",
     "start_time": "2020-06-21T17:35:42.958616Z"
    }
   },
   "outputs": [],
   "source": [
    "def compute_gradients(X, y_true, w_h, b_h, w_o, b_o):\n",
    "    \"\"\"Evaluate gradients for parameter updates\"\"\"\n",
    "\n",
    "    # Compute hidden and output layer activations\n",
    "    hidden_activations = hidden_layer(X, w_h, b_h)\n",
    "    y_hat = output_layer(hidden_activations, w_o, b_o)\n",
    "\n",
    "    # Compute the output layer gradients\n",
    "    loss_grad = loss_gradient(y_hat, y_true)\n",
    "    out_weight_grad = output_weight_gradient(hidden_activations, loss_grad)\n",
    "    out_bias_grad = output_bias_gradient(loss_grad)\n",
    "\n",
    "    # Compute the hidden layer gradients\n",
    "    hidden_layer_grad = hidden_layer_gradient(hidden_activations, w_o, loss_grad)\n",
    "    hidden_weight_grad = hidden_weight_gradient(X, hidden_layer_grad)\n",
    "    hidden_bias_grad = hidden_bias_gradient(hidden_layer_grad)\n",
    "\n",
    "    return [hidden_weight_grad, hidden_bias_grad, out_weight_grad, out_bias_grad]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check Gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's easy to make mistakes with the numerous inputs to the backpropagation algorithm. A simple way to test for accuracy is to compare the change in the output for slightly perturbed parameter values with the change implied by the computed gradient (see [here](http://ufldl.stanford.edu/wiki/index.php/Gradient_checking_and_advanced_optimization) for more detail)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:43.345839Z",
     "start_time": "2020-06-21T17:35:42.969867Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No gradient errors found\n"
     ]
    }
   ],
   "source": [
    "# change individual parameters by +/- eps\n",
    "eps = 1e-4\n",
    "\n",
    "# initialize weights and biases\n",
    "params = initialize_weights()\n",
    "\n",
    "# Get all parameter gradients\n",
    "grad_params = compute_gradients(X, Y, *params)\n",
    "\n",
    "# Check each parameter matrix\n",
    "for i, param in enumerate(params):\n",
    "    # Check each matrix entry\n",
    "    rows, cols = param.shape\n",
    "    for row in range(rows):\n",
    "        for col in range(cols):\n",
    "            # change current entry by +/- eps\n",
    "            params_low = deepcopy(params)\n",
    "            params_low[i][row, col] -= eps\n",
    "\n",
    "            params_high = deepcopy(params)\n",
    "            params_high[i][row, col] += eps\n",
    "\n",
    "            # Compute the numerical gradient\n",
    "            loss_high = loss(forward_prop(X, *params_high), Y)\n",
    "            loss_low = loss(forward_prop(X, *params_low), Y)\n",
    "            numerical_gradient = (loss_high - loss_low) / (2 * eps)\n",
    "\n",
    "            backprop_gradient = grad_params[i][row, col]\n",
    "            \n",
    "            # Raise error if numerical and backprop gradient differ\n",
    "            assert np.allclose(numerical_gradient, backprop_gradient), ValueError(\n",
    "                    f'Numerical gradient of {numerical_gradient:.6f} not close to '\n",
    "                    f'backprop gradient of {backprop_gradient:.6f}!')\n",
    "\n",
    "print('No gradient errors found')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Train Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:43.351161Z",
     "start_time": "2020-06-21T17:35:43.347371Z"
    }
   },
   "outputs": [],
   "source": [
    "def update_momentum(X, y_true, param_list,\n",
    "                    Ms, momentum_term,\n",
    "                    learning_rate):\n",
    "    \"\"\"Update the momentum matrices.\"\"\"\n",
    "    # param_list = [hidden_weight, hidden_bias, out_weight, out_bias]\n",
    "    # gradients = [hidden_weight_grad, hidden_bias_grad,\n",
    "    #               out_weight_grad, out_bias_grad]\n",
    "    gradients = compute_gradients(X, y_true, *param_list)\n",
    "    return [momentum_term * momentum - learning_rate * grads\n",
    "            for momentum, grads in zip(Ms, gradients)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:43.361182Z",
     "start_time": "2020-06-21T17:35:43.352043Z"
    }
   },
   "outputs": [],
   "source": [
    "def update_params(param_list, Ms):\n",
    "    \"\"\"Update the parameters.\"\"\"\n",
    "    # param_list = [Wh, bh, Wo, bo]\n",
    "    # Ms = [MWh, Mbh, MWo, Mbo]\n",
    "    return [P + M for P, M in zip(param_list, Ms)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:43.369778Z",
     "start_time": "2020-06-21T17:35:43.362154Z"
    }
   },
   "outputs": [],
   "source": [
    "def train_network(iterations=1000, lr=.01, mf=.1):\n",
    "    # Initialize weights and biases\n",
    "    param_list = list(initialize_weights())\n",
    "\n",
    "    # Momentum Matrices = [MWh, Mbh, MWo, Mbo]\n",
    "    Ms = [np.zeros_like(M) for M in param_list]\n",
    "\n",
    "    train_loss = [loss(forward_prop(X, *param_list), Y)]\n",
    "    for i in range(iterations):\n",
    "        if i % 1000 == 0: print(f'{i:,d}', end=' ', flush=True)\n",
    "        # Update the moments and the parameters\n",
    "        Ms = update_momentum(X, Y, param_list, Ms, mf, lr)\n",
    "\n",
    "        param_list = update_params(param_list, Ms)\n",
    "        train_loss.append(loss(forward_prop(X, *param_list), Y))\n",
    "\n",
    "    return param_list, train_loss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:35:43.384296Z",
     "start_time": "2020-06-21T17:35:43.371110Z"
    }
   },
   "outputs": [],
   "source": [
    "# n_iterations = 20000\n",
    "# results = {}\n",
    "# for learning_rate in [.01, .02, .05, .1, .25]:\n",
    "#     for momentum_factor in [0, .01, .05, .1, .5]:\n",
    "#         print(learning_rate, momentum_factor)\n",
    "#         trained_params, train_loss = train_network(iterations=n_iterations, lr=learning_rate, mf=momentum_factor)\n",
    "#         results[(learning_rate, momentum_factor)] = train_loss[::1000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:49:10.666152Z",
     "start_time": "2020-06-21T17:35:43.385375Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000 12,000 13,000 14,000 15,000 16,000 17,000 18,000 19,000 20,000 21,000 22,000 23,000 24,000 25,000 26,000 27,000 28,000 29,000 30,000 31,000 32,000 33,000 34,000 35,000 36,000 37,000 38,000 39,000 40,000 41,000 42,000 43,000 44,000 45,000 46,000 47,000 48,000 49,000 "
     ]
    }
   ],
   "source": [
    "trained_params, train_loss = train_network(iterations=n_iterations, \n",
    "                                           lr=learning_rate, \n",
    "                                           mf=momentum_factor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:49:10.669415Z",
     "start_time": "2020-06-21T17:49:10.667324Z"
    }
   },
   "outputs": [],
   "source": [
    "hidden_weights, hidden_bias, output_weights, output_bias = trained_params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot Training Loss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot displays the training loss over 50K iterations for 50K training samples with a momentum term of 0.5 and a learning rate of 1e-4. \n",
    "\n",
    "It shows that it takes over 5K iterations for the loss to start to decline but then does so very fast. We have not uses stochastic gradient descent, which would have likely significantly accelerated convergence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:49:11.510359Z",
     "start_time": "2020-06-21T17:49:10.671272Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = pd.Series(train_loss).plot(figsize=(12, 3), title='Loss per Iteration', xlim=(0, n_iterations), logy=True)\n",
    "ax.set_xlabel('Iteration')\n",
    "ax.set_ylabel('$\\\\log \\\\xi$', fontsize=12)\n",
    "sns.despine()\n",
    "plt.tight_layout()\n",
    "plt.savefig(results_path / 'ffnn_loss', dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Decision Boundary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following plots show the function learned by the neural network with a three-dimensional hidden layer form two-dimensional data with two classes that are not linearly separable as shown on the left. The decision boundary misclassifies very few data points and would further improve with continued training. \n",
    "\n",
    "The second plot shows the representation of the input data learned by the hidden layer. The network learns hidden layer weights so that the projection of the input from two to three dimensions enables the linear separation of the two classes. \n",
    "\n",
    "The last plot shows how the output layer implements the linear separation in the form of a cutoff value of 0.5 in the output dimension."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:49:12.408123Z",
     "start_time": "2020-06-21T17:49:11.511897Z"
    }
   },
   "outputs": [],
   "source": [
    "n_vals = 200\n",
    "x1 = np.linspace(-1.5, 1.5, num=n_vals)\n",
    "x2 = np.linspace(-1.5, 1.5, num=n_vals)\n",
    "xx, yy = np.meshgrid(x1, x2)  # create the grid\n",
    "\n",
    "# Initialize and fill the feature space\n",
    "feature_space = np.zeros((n_vals, n_vals))\n",
    "for i in range(n_vals):\n",
    "    for j in range(n_vals):\n",
    "        X_ = np.asarray([xx[i, j], yy[i, j]])\n",
    "        feature_space[i, j] = np.argmax(predict(X_, *trained_params))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:49:36.361843Z",
     "start_time": "2020-06-21T17:49:35.586519Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a color map to show the classification colors of each grid point\n",
    "cmap = ListedColormap([sns.xkcd_rgb[\"pale red\"],\n",
    "                       sns.xkcd_rgb[\"denim blue\"]])\n",
    "\n",
    "# Plot the classification plane with decision boundary and input samples\n",
    "plt.contourf(xx, yy, feature_space, cmap=cmap, alpha=.25)\n",
    "\n",
    "# Plot both classes on the x1, x2 plane\n",
    "data = pd.DataFrame(X, columns=['$x_1$', '$x_2$']).assign(Class=pd.Series(y).map({0:'negative', 1:'positive'}))\n",
    "sns.scatterplot(x='$x_1$', y='$x_2$', hue='Class', data=data, style=y, markers=['_', '+'], legend=False)\n",
    "plt.title('Decision Boundary')\n",
    "sns.despine()\n",
    "plt.tight_layout()\n",
    "plt.savefig(results_path / 'boundary', dpi=300);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Projection on Hidden Layer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:49:39.197277Z",
     "start_time": "2020-06-21T17:49:39.194418Z"
    }
   },
   "outputs": [],
   "source": [
    "n_vals = 25\n",
    "x1 = np.linspace(-1.5, 1.5, num=n_vals)\n",
    "x2 = np.linspace(-1.5, 1.5, num=n_vals)\n",
    "xx, yy = np.meshgrid(x1, x2)  # create the grid\n",
    "X_ = np.array([xx.ravel(), yy.ravel()]).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:49:40.019824Z",
     "start_time": "2020-06-21T17:49:39.505435Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(6, 4))\n",
    "with sns.axes_style(\"whitegrid\"):\n",
    "    ax = Axes3D(fig)\n",
    "\n",
    "ax.plot(*hidden_layer(X[y == 0], hidden_weights, hidden_bias).T,\n",
    "        '_', label='negative class', alpha=0.75)\n",
    "ax.plot(*hidden_layer(X[y == 1], hidden_weights, hidden_bias).T,\n",
    "        '+', label='positive class', alpha=0.75)\n",
    "\n",
    "ax.set_xlabel('$h_1$', fontsize=12)\n",
    "ax.set_ylabel('$h_2$', fontsize=12)\n",
    "ax.set_zlabel('$h_3$', fontsize=12)\n",
    "ax.view_init(elev=30, azim=-20)\n",
    "# plt.legend(loc='best')\n",
    "plt.title('Projection of X onto the hidden layer H')\n",
    "sns.despine()\n",
    "plt.tight_layout()\n",
    "plt.savefig(results_path / 'projection3d', dpi=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Network Output Surface Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:49:42.447127Z",
     "start_time": "2020-06-21T17:49:42.434598Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(25, 25)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "zz = forward_prop(X_, hidden_weights, hidden_bias, output_weights, output_bias)[:, 1].reshape(25, -1)\n",
    "zz.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-06-21T17:49:43.593470Z",
     "start_time": "2020-06-21T17:49:43.217042Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "with sns.axes_style(\"whitegrid\"):\n",
    "    ax = fig.gca(projection='3d')\n",
    "ax.plot_surface(xx, yy, zz, alpha=.25)\n",
    "ax.set_title('Learned Function')\n",
    "ax.set_xlabel('$x_1$', fontsize=12)\n",
    "ax.set_ylabel('$x_2$', fontsize=12)\n",
    "ax.set_zlabel('$y$', fontsize=12)\n",
    "ax.view_init(elev=45, azim=-20)\n",
    "sns.despine()\n",
    "fig.tight_layout()\n",
    "fig.savefig(results_path / 'surface', dpi=300);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To sum up: we have seen how a very simple network with a single hidden layer with three nodes and a total of 17 parameters is able to learn how to solve a non-linear classification problem using backprop and gradient descent with momentum. \n",
    "\n",
    "We will next review key design choices useful to design and train more complex architectures before we turn to popular deep learning libraries that facilitate the process by providing many of these building blocks and automating the differentiation process to compute the gradients and implement backpropagation."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:ml4t-dl]",
   "language": "python",
   "name": "conda-env-ml4t-dl-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": true,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {
    "height": "calc(100% - 180px)",
    "left": "10px",
    "top": "150px",
    "width": "254px"
   },
   "toc_section_display": true,
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
